Question

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by

• A. $\sqrt { 2 } \mathrm { Mg }$
• B. $\sqrt { 2 } \mathrm { mg }$
• C. $g \sqrt { ( M + m ) ^ { 2 } + m ^ { 2 } }$
• D. $g \sqrt { ( M + m ) ^ { 2 } + M ^ { 2 } }$

Answer 1

Answer: (D)

$g \sqrt { ( M + m ) ^ { 2 } + M ^ { 2 } }$

Answer 2

Force applied by clamp = resultant of T and (mg + T)

But T = Mg

∴ Force applied by clamp

= $\sqrt { ( \mathrm { Mg } ) ^ { 2 } + ( \mathrm { mg } + \mathrm { Mg } ) ^ { 2 } }$ = g $\sqrt { M ^ { 2 } + ( M + m ) ^ { 2 } }$